A385688 E.g.f. A(x) satisfies A(x) = exp( x*((A(x) + A(-x))/2)^3 ).

1, 1, 1, 10, 37, 736, 4861, 145552, 1392553, 55772416, 700205401, 35139710464, 546584937229, 32977620613120, 612127803448981, 43150087404292096, 930914421449463505, 75083676142358560768, 1846230024226716759601, 167681514857730519728128, 4629062510444281987051381

Offset: 0

Author

Seiichi Manyama, Jul 06 2025

Keywords

• nonn

Crossrefs

Cf. A058014, A385687.

Cf. A143547, A360988.

Programs

Mathematica

terms = 21; A[] = 1; Do[A[x] = Exp[x*((A[x] + A[-x])/2)^3] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* Stefano Spezia, Jul 07 2025 *)

Formula

E.g.f. A(x) satisfies A(-x) = 1/A(x).

a(0) = 1; a(n) = (n-1)! * Sum_{i, j, k, l>=0 and i+2*j+2*k+2*l=n-1} (n-i) * a(i) * a(2*j) * a(2*k) * a(2*l)/(i! * (2*j)! * (2*k)! * (2*l)!).